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I'm very new to quantum mechanics and have purchased 'Quantum Mechanics: The Theoretical Minimum. I'm still a bit confused by a fairly fundamental idea.

In the book, it states that you first prepare a spin state (say the σz = +1) in the initial measurement. If you rotate the apparatus by 90 degrees then measure again, a +1 or -1 measurement will be produced (with a statistical average of repeated measurements being 0, I'm happy with that). Let's say the apparatus produced σ = -1. My question is, is the system now 'prepared' in this new direction? If you simply measured the spin again without resetting the spin or apparatus, would you produce the same measurement of σ = -1 again and again?

In the book, it says 'The intermediate measurement along the x axis will leave the spin in a completely random configuration as far as the next measurement is concerned.' If someone could clarify this for me please, I would greatly appreciate it!

Thanks!